Cellular structures in the shape of auxetic honeycombs are characterized by negative Poisson's ratios. These structures offer interesting properties such as indentation resistance, shear resistance and an ability to absorb mechanical energy under impact. Optimizing such structures can lead to innovative design solutions. As part of this study, the interest is focused on the shape optimizing of auxetic unit cells in the form of honeycombs. The objective is to implement an optimization procedure which associates Abaqus and Matlab software in order to demonstrate the effectiveness of the Abaqus2Matlab toolbox. The obtained numerical results were consistent with the analytical results conducted on the basis of the work of Gibson and Ashby. The accuracy of results based on the implemented shape optimization procedure constitutes a preliminary brick towards designing architectured 2D structures